Orders in power semigroups

Maximal Orders In Completely 0-simple Semigroups

Fountain, Gould and Smith introduced the concept of equivalence of orders in a semigroup and the notion of a maximal order. We examine these ideas in the context of orders in completely 0-simple semigroups with particular emphasis on abundant orders.

Power centralized semigroups

A semigroup is said to be power centralized if for any pair of elements there exists a power of the first one commuting with the second one. We describe the structure of power centralized groups and semigroups. In particular, we present several characterizations of periodic semigroups with central idempotents.

On Power Γ-Semigroups

Let S1 and S2 be Γ-semigroups. In this note, we determine when S1 and S2 are isomorphic if the power semigroup of S1 and the power semigroup of S2 are o-isomorphic.

Quasi-orders and Semilattice Decompositions of Semigroups (A Survey)

Power Semigroups: Results and Problems

This is a survey of work on the algebraic theory of the power operator on pseudovarieties of semigroups and monoids. Besides exploring connections with other operators, various problems and partial solutions are presented. Recent generalizations of the power operator, particularly the one resulting from looking only at group-pointlike subsets of nite monoids, are also considered.